Computational Methods

__Path-Integral Monte Carlo__. This technique
is used to study atoms deposited on surfaces.

A good reference for this technique is our paper:

"Path-integral Monte Carlo simulation of the second
layer of 4He adsorbed on graphite".

M. Pierce and E. Manousakis

Phys. Rev. B 59, 3802 (1999) [View:PDF
(1 MB)]

__Green's function Monte Carlo__. This
techniques is used to study the ground state

of correlated systems. A recentl publication
which describes the technique and gives

references is the following.

"Green's function Monte Carlo for Lattice Fermions: Application
to the t-J Model".

C. S. Hellberg and E. Manousakis, Phys.
Rev. B 61, 11787 (2000).

We also use __Monte Carlo methods for classical
models.__

If the order parameter has been correctly
identified, such models

can describe the critical properties of quantum
phase transitions

within the context of Landau-Ginzburg theory
of phase transitions.

Related references can be found in

"Finite-size scaling in two-dimensional superfluids"

N. Schultka and E. Manousakis

Phys. Rev. B 49, 12071-12077 (1994)
[View Page Images, PDF
(639 kB)]

We also use __exact diagonalization techniques.__

See for example the following publication.

"Stripes and the t-J Model "

C. Stephen Hellberg and E. Manousakis

Phys. Rev. Lett. 83, 132 (1999). [View:
PDF (1MB)]

While the solution provided by such method is
exact for the

ground state or a few low-lying excited states,
only small

size systems can be studied by the method.

Since we are interested for properties in the
thermodynamic

limit, the results obtained with this technique
have to be taken

with great caution.